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81.
A. H.M. Rahmatullah Imon 《Journal of applied statistics》2009,36(3):347-358
The heterogeneity of error variance often causes a huge interpretive problem in linear regression analysis. Before taking any remedial measures we first need to detect this problem. A large number of diagnostic plots are now available in the literature for detecting heteroscedasticity of error variances. Among them the ‘residuals’ and ‘fits’ (R–F) plot is very popular and commonly used. In the R–F plot residuals are plotted against the fitted responses, where both these components are obtained using the ordinary least squares (OLS) method. It is now evident that the OLS fits and residuals suffer a huge setback in the presence of unusual observations and hence the R–F plot may not exhibit the real scenario. The deletion residuals based on a data set free from all unusual cases should estimate the true errors in a better way than the OLS residuals. In this paper we propose ‘deletion residuals’ and the ‘deletion fits’ (DR–DF) plot for the detection of the heterogeneity of error variances in a linear regression model to get a more convincing and reliable graphical display. Examples show that this plot locates unusual observations more clearly than the R–F plot. The advantage of using deletion residuals in the detection of heteroscedasticity of error variance is investigated through Monte Carlo simulations under a variety of situations. 相似文献
82.
CECILIA MANCINI 《Scandinavian Journal of Statistics》2009,36(2):270-296
Abstract. We consider a stochastic process driven by diffusions and jumps. Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred. This allows us to determine a consistent non‐parametric estimator of the integrated volatility when the infinite activity jump component is Lévy. Jump size estimation and central limit results are proved in the case of finite activity jumps. Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data. 相似文献
83.
Results are developed concerning the asymptotic behaviour of the Bayes classification rule as the number of unclassified observations grows without bound. It is shown that unclassified observations serve only to estimate the individual population parameters in an unlabeled sense and do not provide information about the labels that are attached to the populations. Prior construction is approached through investigation of prior odds over regions of the joint parameter space (across all populations) deemed likely to contain the true joint parameter vector. It is shown that consideration of these prior odds can lead to more robust a posteriori classification of individual observations. 相似文献
84.
The problem considered is that of finding an optimum measurement schedule to estimate population parameters in a nonlinear model when the patient effects are random. The paper presents examples of the use of sensitivity functions, derived from the General Equivalence Theorem for D-optimality, in the construction of optimum population designs for such schedules. With independent observations, the theorem applies to the potential inclusion of a single observation. However, in population designs the observations are correlated and the theorem applies to the inclusion of an additional measurement schedule. In one example, three groups of patients of differing size are subject to distinct schedules. Numerical, as opposed to analytical, calculation of the sensitivity function is advocated. The required covariances of the observations are found by simulation. 相似文献
85.
Popularity among peers might be related to behavior in gradual or non‐gradual ways. In this research, a popularity subgroups approach was used to examine whether some behaviors were associated with only specific levels of popularity. Moreover, observational data in popularity research is valuable yet scarce. This research, therefore, also examined the association between popularity and observed behavior in a cooperative and competitive setting. In total, 182 early adolescents (58.2% girls, Mage = 10.7 years) completed peer nominations and were observed during a cooperative and a competitive task in groups of four. Results show that affective ties increased gradually with increasing popularity, but that relational aggression, bullying and attention‐attracting qualities distinguished popular adolescents from other early adolescents, and victimization distinguished unpopular adolescents from the other early adolescents. Observations showed that high popularity was defined by high levels of negative behavior, prosocial resource control, skillful leadership, and influence, with the effect of popularity on influence being stronger in the cooperative than the competitive setting. Using multiple methods, and taking context into account, a more complete behavioral profile of different levels of popularity is provided. 相似文献
86.
87.
Saul Blumentthal 《统计学通讯:理论与方法》2013,42(11):3607-3628
Data which is grouped and truncated is considered. We are given numbers n1<…<nk=n and we observe Xni ),i=1,…k, and the tottal number of observations available (N> nk is unknown. If the underlying distribution has one unknown parameter θ which enters as a scale parameter, we examine the form of the equations for both conditional, unconditional and modified maximum likelihood estimators of θ and N and examine when these estimators will be finite, and unique. We also develop expressions for asymptotic bias and search for modified estimators which minimize the maximum asymptotic bias. These results are specialized tG the zxponential distribution. Methods of computing the solutions to the likelihood equatims are also discussed. 相似文献
88.
Dibyen Majumdar 《统计学通讯:理论与方法》2013,42(11):3687-3703
A-optimal and mv optimal repeated measurments designs for comparing serveral test treatments with a control are considered. the models considered are basically of two types: without preperides and the cirular model. It is shown known that some known strongly balanced uniform repeated measurements designs can be modified to obtain optimal designs for this problem. Some other methods of finding optimal designs are also given. 相似文献
89.
D. B. Holiday 《统计学通讯:理论与方法》2013,42(6):2107-2124
A kernel estimator of a derivative of arbitrary order of a nonparametric average population curve is considered for a correlated-errors model with balanced replicate measurements at each design point. Asymptotic expansions of the mean squared error are derived for two classes of correlation functions in the model. Consistency, choice of smoothing parameter, and rates of convergence are examined for the important special cases of estimating the first and second derivatives. 相似文献
90.
J.A. Hartigan 《统计学通讯:理论与方法》2013,42(8):2745-2756
Product partition models assume that observations in different components of a random partition of the data are independent given the partition. If the probability distribution of random partitions is in a certain product form prior to making the observations, it is also in product form given the observations. The product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold; and inference about particular future observations may then be made by first conditioning on the partition, and then averaging over all partitions. This model is applied to fatalities in manned rocket launches, using data from the SOYUZ, APOLLO, SHUTTLE, and post-Challenger SHUTTLE programs in the Soviet Union and the United States. The combination of these data suggest that the chance of a fatality in the next shuttle, launch is about .03, after allowing for the possibility that the older programs are of slight relevance to the present shuttle program. 相似文献